Method to optimize perforations for hydraulic fracturing in anisotropic earth formations

ABSTRACT

The subject disclosure relates to determining an optimum orientation for perforations around the circumference of a subsurface borehole and optimum wellbore fluid initiation pressure for hydraulic fracturing in anisotropic formations.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/586,712 filed Aug. 15, 2012, which claims priority to U.S.Provisional Application No. 61/524,042 filed Aug. 16, 2011, entitled“METHOD TO OPTIMIZE PERFORATIONS FOR HYDRAULIC FRACTURING IN ANISOTROPICEARTH FORMATIONS,” to Romain Prioul et al., the disclosures of which areincorporated by reference herein in their entireties.

FIELD

The subject disclosure generally relates to the field of geosciences.More particularly, the subject disclosure relates to the determinationof the orientation around the circumference of a subsurface borehole andthe wellbore fluid initiation pressure that is optimum for perforationoperations for hydraulic fracturing in anisotropic formations.

BACKGROUND

Perforation techniques are widely used in the oil and gas industry bothfor enhancing hydrocarbon production by minimizing sand production andfor hydraulic fracture stimulation initiation. Citing a comprehensivereview on the topic, “the process of optimizing stimulation treatmentsuses orientated perforations to increase the efficiency of pumpingoperations, reduce treatment failures and improve fractureeffectiveness. Completion engineers develop oriented-perforatingstrategies that prevent sand production and enhance well productivity byperforating to intersect natural fractures or penetrate sectors of aborehole with minimal formation damage.” See Almaguer et al., “Orientingperforations in the right direction”, Oilfield Review, Volume 1, Issue1, Mar. 1, 2002.

Hydraulic fractures initiate and propagate from positions around thecircumference of the open borehole wall that offer the least resistancein terms of stress and rock strength conditions. If the formationmaterial properties (e.g. elastic stiffness and strength) are isotropicand homogeneous and if the material is intact (free of natural fracturesor flaws), it is generally accepted that the fracture initiation occursat the locus around the borehole where the tensile stress is maximum.The stress conditions at the borehole wall in such formation depends onthe local stress orientations and magnitudes (local principal stresstensor), the orientation of the borehole and a material property calledPoisson's ratio (if the formation is assumed elastic).

One definition of an optimum perforation orientation is the orientationaround the circumference of a subsurface borehole wall and the wellborefluid initiation pressure that corresponds to the minimum principalstress at the borehole wall (rock mechanics convention is chosen herewith positive compressive stress) reaching the tensile strength of therock. Consequently, the optimum perforation orientation will ultimatelylower the treatment pressure during hydraulic fracturing thereforelowering the energy requirement of a job. It will also result in a“smoother” fracture near the wellbore (i.e. less near wellboretortuosity) in which proppant can be placed more effectively.

Perforation orientations may be designed with the following typicalsteps:

-   1. A rock property called Poisson's ratio v is estimated along the    well most commonly using compressional V_(p) and shear V_(s) sonic    log data from formula ν=0.5(V_(p) ²-2V_(s) ²)/(V_(p) ²-V_(s) ²).    Other methods may also be used as is known in the art.-   2. The far-field stress field (or tensor), σ, and pore pressure,    P_(p), are characterized using direct or indirect stress    measurements, leading to three principal stress directions and    magnitudes (σ₁>σ₂>σ₃) in the subsurface. When one principal stress    is vertical and called σ_(v), the following convention is used    σ_(H), and σ_(h) for, respectively, the maximum and minimum    horizontal principal stresses. For a recent review of the existing    methods, see Hudson, J. A., F. H. Cornet, R. Christiansson, “ISRM    Suggested Methods for rock stress estimation Part 1: Strategy for    rock stress estimation”, International Journal of Rock Mechanics &    Mining Sciences 40 (2003) 991998; Sjoberg, J., R.    Christiansson, J. A. Hudson, “ISRM Suggested Methods for rock stress    estimation Part 2: Overcoring methods”, International Journal of    Rock Mechanics & Mining Sciences 40 (2003) 9991010; Haimson,    B.C., F. H. Cornet, “ISRM Suggested Methods for rock stress    estimation Part 3: hydraulic fracturing (HF) and/or hydraulic    testing of pre-existing fractures (HTPF)”, International Journal of    Rock and U.S. Pat. No.: 8,117,014 to Prioul et al., entitled    “Methods to estimate subsurface deviatoric stress characteristics    from borehole sonic log anisotropy directions and image log failure    directions”.-   3. Given known well orientation as a function of depth, defined by    two angles (well azimuth and deviation), the principal stress tensor    σ=[(σ₁0 0 ; 0 σ₂0 ; 0 0 σ₃] can be transformed using tensor rotation    into a wellbore frame for example using so-called TOH-frame stress    tensor σ_(TOH)=[σ_(xx) ^(TOH)σ_(xy) ^(TOH)σ_(xz) ^(TOH); σ_(xy)    ^(TOH)σ_(yy) ^(TOH)σ_(yz) ^(TOH); σ_(xz) ^(TOH)σ_(yz) ^(TOH)σ_(zz)    ^(TOH)]. The TOH (top of the hole) frame is a coordinate system tied    to the tool/borehole. Hence, its x- and y-axes are contained in the    plane perpendicular to the tool/borehole, and the z-axis is pointing    along the borehole in the direction of increasing depth. The x-axis    of the TOH frame is pointing to the top of the borehole, the y-axis    is found by rotating the x-axis 90 degrees in the tool plane in a    direction dictated by the right hand rule (thumb pointing in the    positive z-direction). Given a known internal wellbore pressure,    P_(W), borehole stresses (or near-field) are then computed using    well-known Kirsch analytical expressions, (See Ernst Gustav Kirsch.    Die Theorie der Elastizitat and die Bedurfnisse der    Festigkeitslehre. “Zeitschrift des Vereines Deutscher Ingenieure”,    42(29):797-807, 1898; Y. Hiramatsu and Y. Oka. “Stress around a    shaft or level excavated in ground with a three-dimensional stress    state”; Kyoto Teikoku Daigaku Koka Daigaku kiyo, page 56, 1962; Y.    Hiramatsu and Y. Oka. “Determination of the stress in rock    unaffected by boreholes or drifts, from measured strains or    deformations”, International Journal of Rock Mechanics and Mining    Sciences & Geomechanics Abstracts, volume 5, pages 337-353.    Elsevier, 1968), for the total stresses at the borehole wall for an    arbitrary orientation of the borehole relative to the far-field    in-situ stress tensor, as follows in cylindrical coordinates:

σ_(rr)=P_(w),

σ_(θθ)=σ_(xx) ^(TOH)+σ_(yy) ^(TOH)−σ_(yy) ^(TOH)) cos 2θ−4σ_(xy) ^(TOH)sin 2θ−P_(w),

σ_(zz)=σ_(zz) ^(TOH)−2ν(σ_(xx) ^(TOH)−σ_(yy) ^(TOH)) cos 2θ−4νσ_(xy)^(TOH) sin 2θ,

σ_(θz)=2(σ_(yz) ^(TOH) cos θ−σ_(xz) ^(TOH) sin θ),

σ_(r)θ=σ_(rz)=0,

where ν is the Poisson's ratio, θ is the azimuthal angle around theborehole circumference measured clockwise from a reference axis (e.g.TOH). Equations to compute borehole stresses away from the borehole wallat a desired radial position into the formation are also available.

-   4. Then, the ideal perforation orientation for tensile initiation is    found for the azimuthal position θ_(t) and the wellbore fluid    initiation pressure P_(w) ^(init) where the minimum principal stress    at the borehole wall is given by

${\sigma_{t} = {{\frac{\sigma_{zz} + \sigma_{\theta\theta}}{2} - \sqrt{\left( \frac{\sigma_{zz} + \sigma_{\theta\theta}}{2} \right)^{2} + \sigma_{\theta z}^{2}}} = {{{- T}\; o} + {P\; p}}}},$

where To is the tensile strength of the rock and Pp is the porepressure.

-   5. Once the optimum orientation is known a perforation tool is    lowered in the well. The perforation tool perforates the well in an    optimum orientation obtained from the previous step.

For a stress field with one principal stress that is vertical (σv), weconsider the special cases of well orientations where the azimuthalposition θ_(t) is always in a principal direction:

-   (a) For vertical wells, the azimuthal position θ_(t) is the minimum    hoop stress (minimum of σ_(θθ)) which is always in the direction of    the maximum horizontal principal stress, σ_(H).-   (b) For horizontal wells drilled in the direction of a principal    stress direction (σ_(H) or σ_(h)), the azimuthal position θ_(t) is    also the one given by the minimum hoop stress (minimum of σ_(θθ)),    i.e. is pointing to the top of the hole if σv is greater than the    horizontal stress orthogonal to the borehole, or to the side of the    hole if σv is smaller than the horizontal stress orthogonal to the    borehole.

If the well is deviated, in such a stress field the orientation is notaligned with a principal stress direction and there is no obvioussolution for θ_(t) as it also depends on the wellbore fluid initiationpressure so the orientation is computed numerically. See Peska, P. &Zoback, M., Compressive and tensile failure of inclined well bores anddetermination of in situ stress and rock strength, Journal ofGeophysical Research, 1995, 100, 12,791-12,811.

When the earth formation has material properties that are directionsdependent, i.e. anisotropic, steps 1, 2 and 3 above are not validanymore and depend on the anisotropy of the rock. Although some studieshave been completed on the impact of the anisotropy on the boreholestress concentration (i.e. step 3), those studies have focused on thewellbore stability issues and mud weight requirements to preventwellbore collapse (shear) and tensile fracturing (tensile), and not on aworkflow to assess the best perforation orientation.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

In embodiments of the subject disclosure methods are disclosed todetermine the optimum orientation for perforations around acircumference of a subsurface borehole and the wellbore fluid initiationpressure that is for hydraulic fracturing in anisotropic formations.

In embodiments of the subject disclosure methods are disclosed fordetermining a perforation orientation for hydraulic fracturing in ananisotropic earth formation. In embodiments the method comprises thesteps of determining anisotropic rock properties; determining far-fieldstresses in the anisotropic earth formation; determining boreholestresses in the anisotropic earth formation; determining an optimumperforation orientation; and perforating a well in the determinedoptimum perforation orientation.

Further features and advantages of the subject disclosure will becomemore readily apparent from the following detailed description when takenin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject disclosure is further described in the detailed descriptionwhich follows, in reference to the noted plurality of drawings by way ofnon-limiting examples of embodiments of the subject disclosure, in whichlike reference numerals represent similar parts throughout the severalviews of the drawings, and wherein:

FIG. 1 illustrates a schematic of the geographic and borehole referenceframes and the principal stress directions;

FIG. 2 illustrates the material coordinate system for a transverseisotropic medium with a tilted symmetry axis (TTI);

FIG. 3 illustrates a workflow for determining perforation orientationsfor hydraulic fracturing in anisotropic earth formations; and

FIG. 4A through 4C illustrate an example of a perforation orientationangle around a borehole.

DETAILED DESCRIPTION

The particulars shown herein are by way of example and for purposes ofillustrative discussion of the embodiments of the subject disclosureonly and are presented in the cause of providing what is believed to bethe most useful and readily understood description of the principles andconceptual aspects of the subject disclosure. In this regard, no attemptis made to show structural details in more detail than is necessary forthe fundamental understanding of the subject disclosure, the descriptiontaken with the drawings making apparent to those skilled in the art howthe several forms of the subject disclosure may be embodied in practice.Furthermore, like reference numbers and designations in the variousdrawings indicate like elements.

Embodiments of the subject disclosure relate to the determination of theorientation around the circumference of a subsurface borehole and thewellbore fluid initiation pressure that is optimum for perforationoperations for hydraulic fracturing in anisotropic formations. In onenon-limiting example, perforation operations include shaped chargeperforation operations.

Embodiments of the subject disclosure comprise methods which areapplicable to arbitrary well orientation, arbitrary stress field andarbitrary elastic anisotropy of a formation.

Embodiments of the subject disclosure disclose a workflow methodcomprising a plurality of steps for determining perforation orientationsfor hydraulic fracturing in anisotropic earth formations. The pluralityof steps include determination of anisotropic rock properties,determination of far-field stresses in anisotropic formations,determination of borehole stresses in anisotropic formations,determination of the optimum fracture orientation and optimum initiationpressure, lowering in the well a perforation tool and perforating thewell in the direction of the optimum orientation obtained from theprevious steps. Anisotropic rock properties and far-field stressproperties may vary along the well and borehole stresses may vary alongthe borehole, therefore, the step of determining the borehole stressesin anisotropic formations may be used to select the depth points ofwhere to place perforation clusters for a given hydraulic fracturingstage in rock with similar near-wellbore stresses or similar wellborefluid initiation pressure. Therefore, the step of determining theborehole stresses in anisotropic formations and the borehole stressesmay be used to determine how to place hydraulic fracturing stages alongthe well.

The subject disclosure will be described in greater detail as follows.First, a number of definitions useful to understanding the subjectdisclosure are presented.

DEFINITIONS Geometry and Coordinate Systems:

In the far-field an in-situ stress field is applied where the principalstress tensor takes the form:

$\sigma = \begin{pmatrix}\sigma_{H} & 0 & 0 \\0 & \sigma_{h} & 0 \\0 & 0 & \sigma_{v}\end{pmatrix}$

where σ_(H) and σ_(h) are the maximum and minimum horizontal stresses,respectively, and σ_(v) is the vertical stress. FIG. 1 illustrates aschematic of the geographic and borehole reference frames and theprincipal stress directions. The geographic reference frame is thenorth-east-vertical (NEV) frame whose x-axis points to the north, y-axispoints to the east, and z-axis points downward in vertical direction.The borehole frame is the top-of-hole (TOH) frame whose z-axis pointsalong the borehole in the direction of increasing depth. The x-axis isin the cross-sectional plane and points to the most upward direction,and the y-axis is found by rotating the x-axis 90° in thecross-sectional plane in a direction dictated by the right-hand rule.The orientation of the borehole is defined by the deviation angle α_(D)and the azimuth angle α_(A).

For the sake of simplicity, but without loss of generality, we assumethat the vertical stress σ_(v) is always aligned with the verticalcomponent (V) of the NEV (north-east-vertical) coordinates system. Thehorizontal stress field can be rotated by an angle γ measured between N(north) and σ_(H) towards E (east). For the computation of the boreholestress concentration it is convenient to rotate the stress field in theNEV frame into the top-of-hole borehole coordinate system, hereaftercalled TOH (see definition above), i.e. σ_(TOH)=[σ_(xx) ^(TOH)σ_(xy)^(TOH)σ_(xz) ^(TOH); σ_(xy) ^(TOH)σ_(yy) ^(TOH)σ_(yz) ^(TOH); σ_(xz)^(TOH)σ_(yz) ^(TOH)σ_(zz) ^(TOH)]. The orientation of the borehole isdefined by the deviation angle α_(D) and the azimuth angle α_(A).

Elasticity Equation

The strain components are related to the stress components GU via theconstitutive relation:

ε_(ij)=S_(ijkl)σ_(kl)

where S_(ijkl) is the fourth rank compliance tensor (and as s_(ij) ifthe 6×6 matrix contracted Voigt notation is used). The inverse of thecompliance tensor is the fourth rank stiffness tensor defined asC_(ijkl) (and c_(ij) in Voigt notation). Rotation of the compliancetensor into the TOH frame can be done by applying two Bondtransformations to the 6×6 Voigt notation compliance matrix s_(ij)giving a new matrix noted a_(ij).

Material Anisotropy

Embodiments of the subject disclosure use an anisotropic medium that istransversely isotropic rocks with a titled axis of symmetry (calledhereafter TTI). In general, this is the most typical type of anisotropyencountered in the Earth, although it should be understood that methodsof the subject disclosure are not restricted to TI media. The TTI mediumis described by five elastic constants in different notations as

-   (a) Elasticity notation: c₁₁, c₃₃, c₁₃, c₄₄ and c₆₆ are the five    stiffness coefficients in Voigt notation of the stiffness tensor    entering in the elasticity relationship between stress and strain.    The orientation of the TI plane is defined by two angles as depicted    in FIG. 2, the dip azimuth β_(A) and the dip angle β_(D). FIG. 2    depicts the material coordinate system for transverse isotropic    medium with tilted symmetry axis (called TTI) where β_(D) is the dip    of the transverse isotropy plane and β_(A) is the dip azimuth.-   (b) Engineering notation: E_(v), and E_(h) are the vertical and    horizontal Young's moduli (with respect to TI plane), v_(v) and    v_(h) the vertical and horizontal Poisson's ratios, and G_(v) the    vertical shear moduli. The orientation of the TI plane is also    defined by two angles as depicted in FIG. 2, the dip azimuth and the    dip angle.-   (c) Geophysics notation: Vp0 and Vs0 are respectively the    compressional and shear velocities along the symmetry axis and ε, δ,    γ are three dimensionless parameters (called Thomsen parameters) and    p is the rock bulk density. The orientation of the TI plane is also    defined by two angles as depicted in FIG. 2, the dip azimuth and the    dip angle.    Initiation Pressure In the present disclosure, the failure criterion    used is a tensile strength criterion; therefore, the initiation    pressure will be understood herein as the fluid pressure within the    borehole resulting in the initiation of a tensile crack in a defect    free subsurface material.

Workflow

This subject disclosure considers the following improvements to takeinto account the anisotropic nature of the rocks and is further depictedin the workflow in FIG. 3. FIG. 3 illustrates an embodiment of thesubject disclosure. FIG. 3 illustrates a workflow for determiningperforation orientations for hydraulic fracturing in anisotropic earthformations. The workflow comprises a plurality of steps as illustratedin FIG. 3.

The first step is determination of anisotropic rock properties (301).This step involves (1) the acquisition of wireline or Logging WhileDrilling (LWD) sonic logs with all modes (monopole, dipole and Stoneley)with a 3D deviation survey, and (2) data processing to identify andestimate borehole sonic anisotropy. This step is performed using toolsand procedures which have been described. See U.S. Pat. No.: 6,714,480to Sinha et al, entitled “Determination of anisotropic moduli of earthformations”, U.S. Pat. No.: 6,718,266 to Sinha et al., entitled“Determination of dipole shear anisotropy of earth formations”, U.S.Patent Publication No.: 2009-0210160 to Suarez-Rivera et al. entitled“Estimating horizontal stress from three-dimensional anisotropy” andU.S. Pat. No.: 8,117,014 to Prioul et al, entitled “Methods to estimatesubsurface deviatoric stress characteristics from borehole sonic loganisotropy directions and image log failure directions”. For TTI media,this leads to five elastic constants, e.g. c₁₁, c₃₃, c₁₃, c₄₄ andc_(66,) and two angles (the dip azimuth β_(A) and dip angle β_(D) of theTI plane, as described above). The five elastic constants will definethe stiffness tensor in the TI frame which can be inverted to get thecompliance tensor rotated in the borehole frame and noted a_(ij). Thisstep can be completed for wells of arbitrary orientation.

The second step is the determination of far-field stresses inanisotropic formations (303). In embodiments of the subject disclosureit is assumed that the principal stress field (σ1>σ2>σ3) and the porepressure P_(p) are given but important considerations to estimatefar-field stresses in anisotropic formations are considered. See UnitedStates Patent Publication No.: 2009-0210160 to Suarez-Rivera et al.entitled “Estimating horizontal stress from three-dimensionalanisotropy”. For example, this includes taking into account theanisotropy of the rock in the determination of the gravitationalcomponent of the stress field which leads to a relationship between thevertical and horizontal stresses for a transversely isotropic rocks withvertical axis of symmetry (VTI) or a titled axis of symmetry (TTI, seeFIG. 2 above) such as described respectively by Thiercelin and Plumb(1994, SPE 21847), Amadei & Pan (1992, IJRMMS) and United States PatentPublication No.: 2009-0210160 to Suarez-Rivera et al. entitled“Estimating horizontal stress from three-dimensional anisotropy”. Thestress tensor is rotated in the TOH frame, to get σ_(TOH)=[σ_(xx)^(TOH)σ_(xy) ^(TOH)σ_(xz) ^(TOH); σ_(xy) ^(TOH)σ_(yy) ^(TOH)σ_(yz)^(TOH); σ_(xz) ^(TOH)σ_(yz) ^(TOH)σ_(zz) ^(TOH)].

The third step is the determination of borehole stresses in ananisotropic formation (305). In embodiments of the subject disclosure ageneral solution for the stresses around a borehole in an anisotropicmedium can be found using elasticity results from the superposition ofthe far field in-situ stress tensor σ_(TOH) and the general expressionsfor the borehole-induced stresses (σ_(bi)). See B. Amadei, RockAnisotropy and the theory of stress measurements. Lecture notes inengineering. Springer Verlag, 1983, S. G. Lekhnitskii, Theory ofelasticity of an anisotropic body. MIR Publishers, Moscow, 1963, Gaede,0., Karpfinger, F., Jocker, J. & Prioul, R., Comparison betweenanalytical and 3D finite element solutions for borehole stresses inanisotropic elastic rock, International Journal of Rock Mechanics &Mining Sciences, 2012, 51, 53-63. This step applies to arbitrary wellorientation, arbitrary stress field and arbitrary elastic anisotropy ofthe formation.

-   -   The stress components in the plane orthogonal to the borehole        are in Cartesian coordinates:

σ_(xx,BH)=σ_(xx,TOH)+σ_(xx,bi)=σ_(xx,TOH)+2Re[μ₁ ²φ′₁(z₁)+μ₂²φ′₂(z₂)+λ₃μ₃ ²φ′₃(z₃)]

σ_(yy,BH)=σ_(yy,TOH)σ_(yy,bi)=σ_(yy,TOH)+2Re[φ′₁(z₁)+φ′₂(z₂)+λ₃φ′₃(z₃)]

σ_(xy,BH)=σ_(xy,TOH)+σ_(xy,bi)=σ_(xy,TOH)−2Re[μ₁φ′₁(z₁)+μ₂φ′₂(z₂)+λ₃μ₃φ′₃(z₃)]

σ_(xz,BH)=σ_(xz,TOH)+σ_(xz,bi)=σ_(xz,TOH)+2Re[μ₁μ₁φ′₁(z₁)+λ₂μ₂φ′₂(z₂)+μ₃φ′₃(z₃)]

σ_(yz,BH)=σ_(yz,TOH)+σ_(yz,bi)=σ_(yz,TOH)−2Re[λ₁φ′₁(z₁)+λ₂φ′₂(z₂)+φ′₃(z₃)]

-   -   The stress component in the borehole axis direction is deduced        from the generalized plane stress assumption using the other        stress components and the compliance tensor component a_(ij):

$\sigma_{{zz},{BH}} = {\sigma_{{zz},{TOH}} - {\frac{1}{a_{33}}\left( {{a_{31}\sigma_{{xx},{bi}}} + {a_{32}\sigma_{{yy},{bi}}} + {a_{34}\sigma_{{yz},{bi}}} + {a_{35}\sigma_{{xz},{bi}}} + {a_{36}\sigma_{{xy},{bi}}}} \right)}}$

-   -   The Cartesian stresses are then transformed into cylindrical        coordinates to get σ_(rr), σ_(θθ), σ_(zz), σ_(θz), σ_(rθ),        σ_(rz)    -   These equations include the solutions to compute borehole        stresses away from the borehole wall at a desired radial        position into the formation.        The fourth step is the determination of an optimum perforation        orientation (307). This step is the same as for an isotropic        rock. The ideal perforation orientation for tensile initiation        is found for the azimuthal position θ_(t) and the initiation        pressure P_(w) ^(init) where the minimum principal stress at the        borehole wall is given by

${\sigma_{t} = {{\frac{\sigma_{zz} + \sigma_{\theta\theta}}{2} - \sqrt{\left( \frac{\sigma_{zz} - \sigma_{\theta\theta}}{2} \right)^{2} + \sigma_{\theta z}^{2}}} = {{{- T}\; o} + {P\; p}}}},$

where To is the tensile strength of the rock and Pp is the porepressure. Steps three and four can be performed not only at the boreholewall but at any desired radial position within the formation using theappropriate stress concentration solutions from step 3.

The fifth step is to perforate a well in an optimum orientation (309).Knowing the optimum orientation, a perforation tool may be lowered intoa well, the tool perforating the well in the direction of the optimumorientation obtained from the previous step.

In addition to the previous steps at a given depth point, it isunderstood that since anisotropic rock properties and far-field stressproperties (from steps 1 and 2 above) can vary along the well, boreholestresses (step 3 above) will vary along the borehole and therefore step3 can be used to select the depth points with similar near-wellborestresses or similar wellbore fluid initiation pressure where to placeperforation clusters for a given hydraulic fracturing stage in rock.Therefore, step 3 may be used with the borehole stresses to determinehow to place hydraulic fracturing stages along the well.

EXAMPLE

If the following conditions are considered at a given depth for ahypothetical well:

-   -   The stress field is the result of step 1: σ_(v)=19.98 MPa,        σ_(H)=19.9 MPa, σ_(h)=18.73 MPa, P_(p)=11.63 MPa. σ_(H) is        oriented in the North direction.    -   The anisotropic material properties are the result of step 2:        E_(h)=3.55 GPa, E_(v)=2.13 GPa, ν_(h)=0.4, ν_(v)=0.29,        G_(h)=1.27 GPa. The dip azimuth and dip angle are both zero here        (β_(D)=β_(A)=0).

If we loop over a grid of well orientation with deviation angle between0 and 90° and azimuth between 0 and 360°, we can perform steps 3 and 4for each well orientation to get the ideal azimuthal position θ^(TTI)_(t) and the wellbore fluid initiation pressure P_(w) ^(init) _(TTI). Ifstep 3 of this workflow is replaced by its isotropic version (describedin the background) using the horizontal Poisson's ratio as a materialproperty, we can compute azimuthal position θ^(ISO) _(t) and thewellbore fluid initiation pressure P_(w) ^(init) _(ISO) and compare thedifference between those two angles. Results on FIG. 4A-4C show that thedifference |θ^(TTI) _(t)-θ^(ISO) _(t)| due to the anisotropy of thematerial orientation which can be up to 45° in this example (Differencebetween P_(w) ^(init) _(TTI) and P_(w) ^(init) _(ISO) not shown here,for such details, we refer to Prioul, R., Karpfinger, F., Deenadayalu,C. & Suarez-Rivera, R., Improving Fracture Initiation Predictions onArbitrarily Oriented Wells in Anisotropic Shales, Society of PetroleumEngineers, SPE-147462, 2011, 1, 1-18).

FIG. 4A-C depicts examples of an optimum perforation orientation anglearound a borehole computed using in FIG. 4A isotropic stressconcentration and in FIG. 4B anisotropic stress concentrations. Thedifference between FIG. 4A and FIG. 4B is shown in FIG. 4C. Results areplotted on a polar grid where each point of the grid correspond to wellorientation, with radial variation corresponding to well deviation (from0 to 90) and azimuthal variation corresponding to well azimuth (from 0to 360) with the convention of clockwise positive rotation from North toEast.

Although only a few example embodiments have been described in detailabove, those skilled in the art will readily appreciate that manymodifications are possible in the example embodiments without materiallydeparting from this invention. Accordingly, all such modifications areintended to be included within the scope of this disclosure as definedin the following claims. In the claims, means-plus-function clauses areintended to cover the structures described herein as performing therecited function and not only structural equivalents, but alsoequivalent structures. Thus, although a nail and a screw may not bestructural equivalents in that a nail employs a cylindrical surface tosecure wooden parts together, whereas a screw employs a helical surface,in the environment of fastening wooden parts, a nail and a screw may beequivalent structures. It is the express intention of the applicant notto invoke 35 U.S.C. §112, paragraph 6 for any limitations of any of theclaims herein, except for those in which the claim expressly uses thewords ‘means for’ together with an associated function.

What is claimed is:
 1. A method for determining a perforationorientation for hydraulic fracturing in an anisotropic earth formationcomprising: determining anisotropic rock properties; determiningfar-field stresses in the anisotropic earth formation; determiningborehole stresses in the anisotropic earth formation; and determining anoptimum perforation orientation and optimum wellbore fluid initiationpressure.
 2. The method according to claim 1 further comprisingperforating a well in the determined optimum perforation orientation. 3.The method according to claim 1 wherein the determining anisotropic rockproperties further comprises: acquisition of a sonic log with a 3Ddeviation survey; data processing to characterize borehole sonicanisotropy.
 4. The method according to claim 3 wherein the acquisitionof the sonic log uses a monopole mode.
 5. The method according to claim3 wherein the acquisition of the sonic log uses a dipole mode.
 6. Themethod according to claim 3 wherein the acquisition of the sonic loguses a monopole mode, a dipole mode or a Stoneley mode, or anycombination of
 7. The method according to claim 2 wherein the well is adeviated well.
 8. The method according to claim 2 wherein the well is ahorizontal well.
 9. The method according to claim 2 wherein the well isa vertical well.
 10. The method according to claim 2 wherein theperforating the well in the optimum perforation orientation is performedwith at a shaped charge.
 11. A method for perforating a well traversinga subterranean area including one or more transversely isotropicformations with a tilted axis of symmetry comprising: determiningformation properties; determining far-field stresses in the formation;determining borehole stresses in the formation; determining an optimumperforation orientation and optimum wellbore fluid initiation pressure;and perforating the well in the determined optimum perforationorientation.
 12. The method according to claim 11 wherein the wellcomprises one or more portions of a group consisting of a deviatedportion, a horizontal portion, or a vertical portion.
 13. The methodaccording to claim 11 wherein the perforating of the well is done withone or more shaped charges.
 14. The method according to claim 11 furthercomprising: determination of borehole stresses in the well at differentdepths; positioning perforation clusters at one or more depth pointswith borehole stresses similar to a previous perforation depth; andperforating the well at the one or more depth points for placement ofhydraulic fracturing stages along the well.
 15. A method for hydraulicfracturing in an anisotropic earth formation comprising: determininganisotropic rock properties; determining far-field stresses in theanisotropic earth formation; determining borehole stresses in theanisotropic earth formation; determining an optimum perforationorientation and optimum wellbore fluid initiation pressure; perforatinga well in the determined optimum perforation orientation; and hydraulicfracturing the well at a pressure at least at the optimum wellbore fluidinitiation pressure.
 16. The method according to claim 15 wherein thewell comprises one or more portions of a group consisting of a deviatedportion, a horizontal portion, or a vertical portion.
 17. The method ofclaim 15 in which the determining anisotropic rock properties comprisesacquisition of wireline sonic logs with all modes with a 3D deviationsurvey.
 18. The method of claim 15 in which the determining anisotropicrock properties comprises acquisition of logging while drilling soniclogs with all modes with a 3D deviation survey.
 19. The method of claim15 in which the perforating of the well comprises one or more shapecharges.
 20. The method according to claim 17 wherein the acquisition ofthe sonic log uses a monopole mode, a dipole mode or a Stoneley mode, orany combination of